If you mean by romance, did they fall in love throughout the movie? No. But there is an immediate attraction and admiration for them in various alteregos. When Selina robs Bruce he isn't upset, but bemused. She literally kicks the cane out form under him and wakes him up to the outside world. It's what prompts him to go to the batcave for the first time in years to research her. He says its for the pearls and fingerprints, but it's obvious he is smitten with her and admires her. Alfred even teases him about it. It is one of the key reasons he leaves the estate for the first time in three years. When he appears at the dance, he is genuinely flirting with her and not as his usual act and she is bemused by him and lets him have the pearls (and a kiss) which is more than I'd say she lets her usual marks get away with. She also later allows him into her apartment. And as Catwoman, we see she has some type of fangirl crush on Batman (she would have been a teenager during the events of BB/TDK) given how she reacts to him showing up on the TV and then when she's sitting in the back of the Bat.

And then, yes, she ends up redeeming herself by helping him save the city. When it looks like he's going to die, she acts on her obvious attraction to him by giving him a kiss. Does all this mean they're in passionate love? No. It means they're very obviously attracted to one another and respect/admire the other's abilities. All that said, if they both want to disappear from Gotham can I believe they would give dating a shot? Sure. Why not? It's not like we saw them have kids running around at the end. Though, I do wonder if they did get serious during the intervening months as she is wearing his mother's pearls.

I wish they had more screen time, but I bought the characters and their relationship. So it does work.

I posted this in another thread.

Indeed. The set up was there. The romance happened off camera. She ended up with his mother's pearls. It's not something he would give to a casual friend or fling. Definitely implies significant other.

I actually liked how Nolan handled their relationship without hitting us over the head with it.